The first thing you need to do is make sure you've got access to money for the next few weeks. So if its a joint account, take some cash out for food etc
Check your entitlement to Universal Credit on this website:
https://www.turn2us.org.uk/
Apply now, as the first payment takes 5 weeks to come through. You can always cancel your claim if he comes back.
Have a look at the child maintenance calculator:
https://www.gov.uk/calculate-child-maintenance
Tell him.you are doing this, as that may make him think about what he actually wants.
Apply for a single person council tax reduction.
The turn2us website will tell you if you're entitled to a further council tax reduction due to income. You will need to apply separately so do that if you are eligible.
Apply for a cheaper tariff for water, your supplier will have info on the website. You are usually eligible for this if you have 4 children.
If entitled to Universal Credit, look at getting a cheaper broadband package. Info here:
https://www.ofcom.org.uk/phones-telecoms-and-internet/advice-for-consumers/costs-and-billing/social-tariffs
If your income is low, apply for free school meals. Even if the children get universal free school meals you need to apply for fresh school meals, as the free school meals eligibility entitles you to other grants.
Go through your income/expenditure and see where you can make changes and make a budget.